I'll leave an American to answer number 2.

1. OK, slightly confusing, I know. The UK is the political entity, comprising the countries, provinces or 'constituant entities' England, Wales, Scotland, N. Ireland plus other smaller islands. England is just one of the countries in this grouping so to call someone from Scotland English, for example, would be offensive to them. Only people from England should be called English.  Great Britain - this is the name of the largest island in the group - which contains just England, Wales and Scotland. British - gets used to refer to people from the UK. Some people like 'Brit' (I obviously do) and others hate it, so I'd avoid it unless you know someone likes it.

3. We normally just say 'I think that' or simply state your opinion without any introduction. After all, you are not likely to be telling someone an opinion you do not hold personally. It's more usual to point it out when you are stating someone else's opinion, or if there is a difference of opinion. For example 'I think we should buy a Ford car but Fred would rather get a Vauxhall'.  To say 'In my opinion' can sound rather pompous.

Some people object to using "American" to apply to people who live in the United States of America, saying that there are two continents names America. I think that overwhelming use of "America" to equal the USA - use that exists OUTSIDE of the US as well as inside - is just too strong to overcome. If someone says "I'm an Amerian" not very many people will say "Oh, do you live in South America or North America?"

And of course even on the continent of North America, there are two other countries in addition to the U.S.  Personally, I would identify myself as "an American," but I would be more likely to say "I live in the U.S." or "I live in the United States" rather  than "I live in America."  Especially if I was speaking to a Canadian or  a Mexican!  (And "The U.S." is just easier to say than "the U.S.A.", and I'm not afraid that my listeners will mistake the U.S. for "the United States of anything else" other than America.)

Nona The Brit wrote:

To say 'In my opinion' can sound rather pompous.